Geodesic
Nim-regularity of graphs
The electronic journal of combinatorics, Tome 6 (1999)
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Ehrenborg and Steingrímsson defined simplicial Nim, and defined Nim-regular complexes to be simplicial complexes for which simplicial Nim has a particular type of winning strategy. We completely characterize the Nim-regular graphs by the exclusion of two vertex-induced subgraphs, the graph on three vertices with one edge and the graph on five vertices which is complete except for one missing edge. We show that all Nim-regular graphs have as their basis the set of disjoint unions of circuits (minimal non-faces) of the graph.
DOI : 10.37236/1443
Classification : 91A43, 91A05, 91A44, 91A46
Mots-clés : simplicial Nim, Nim-regular graphs 
@article{10_37236_1443,
     author = {Nathan Reading},
     title = {Nim-regularity of graphs},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1443},
     zbl = {0913.90287},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1443/}
}
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Nathan Reading. Nim-regularity of graphs. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1443

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